The theory that describes how plate tectonics influence the Earth's surface is known as the plate tectonics theory. This scientific theory explains the movement of the Earth's lithosphere, composed of tectonic plates that float on the semi-fluid asthenosphere beneath them. The interactions of these plates can lead to various geological phenomena, including earthquakes, volcanoes, and mountain formation. This theory has significantly advanced our understanding of geological processes and the dynamic nature of the Earth's surface.